Mars has a mass of 6.4 × 1023 kg. It has a moon named Deimos with a mass of 1.48 × 1015 kg.

Question

a. If their centers are 23,460 km apart, what is the force of gravity acting on Deimos? (3 points)

b. Deimos is extremely small, with a radius of just 21 km. What is the acceleration of gravity on the surface of Deimos? (3 points)

c. What is the acceleration of Deimos as it orbits Mars? (3 points)

Answer 1

M = mass of Mars in kg

m = mass of Deimos in kg

d = distance between centers of Mars and Deimos in METERS

G = constant of gravitation (look it up in your book in units of Nm²/kg²)

I will give you the approach for each part.

(a)

F = GMm / d²

Remember to convert the distance d to meters. Now plug in the numbers and get F in newtons.

(b)

r = radius of Deimos in METERS

g' = Gm / r²

Remember to use the given mass of Deimos, and convert the radius of Deimos to meters. G is the same. Plug in the numbers and get g' in m/s².

(c)

It will be the force calculated in part (a) divided by the mass of Deimos.

a = [(GMm) / d²] / m ⇒

a = GM / d²

Plug in the numbers with d in meters and use the mass of Mars.

You should be able to finish from here.